Antithetic variates in higher dimensions

Details Antithetic variates in higher dimensions Antithetic variates in higher dimensions

2009-02-24

arxiv.org/abs/0902.4211v3

Mathematics

Numerical Analysis

18 pages. Some errors were corrected

Scientific paper

We introduce the concept of multidimensional antithetic as the absolute minimum of the covariance defined on the orthogonal group by $A\mapsto Cov(f(\xi),f(A\xi))$ where $\xi$ is a standard $N$-dimensional normal random variable and $f:\mathbb{R}^{N}\to\mathbb{R}$ is an almost everywhere differentiable function. The antithetic matrix is designed to optimise the calculation of $E[f(\xi)]$ in a Monte Carlo simulation. We present an iterative annealing algorithm that dynamically incorporates the estimation of the antithetic matrix within the Monte Carlo calculation.

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